Applied Mathematics Letters最新文献

{"title":"Threshold behavior of a stochastic predator–prey model with fear effect and regime-switching","authors":"Jing Ge,&nbsp;Weiming Ji,&nbsp;Meng Liu","doi":"10.1016/j.aml.2025.109476","DOIUrl":"10.1016/j.aml.2025.109476","url":null,"abstract":"<div><div>This work proposes a stochastic predator–prey model with fear effect and regime-switching. It is testified that the dynamical behaviors of the model are determined by two thresholds <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><mi>G</mi></math></span>: if both <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><mi>G</mi></math></span> are positive, then the model admits a unique stationary distribution with the ergodic property; if <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is positive and <span><math><mi>G</mi></math></span> is negative, then the predator population dies out and the prey population is persistent; if <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is negative, then both the prey population and the predator population die out. Some recent results are improved and extended greatly.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109476"},"PeriodicalIF":2.9,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Positive recurrence of a stochastic heroin epidemic model with standard incidence and telegraph noise","authors":"Yu Chen,&nbsp;Xiaofeng Zhang","doi":"10.1016/j.aml.2025.109474","DOIUrl":"10.1016/j.aml.2025.109474","url":null,"abstract":"<div><div>The heroin epidemic has posed a serious threat to public health and social stability. Understanding the dynamics of the heroin epidemic model is of great significance for formulating effective prevention and control strategies. In this paper, a stochastic heroin epidemic model with standard incidence and telegraph noise is considered. By constructing a suitable stochastic Lyapunov function with regime switching, we get sufficient conditions of positive recurrence of the solution for stochastic system, which may provide valuable insights for further research and control strategies related to heroin epidemics.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109474"},"PeriodicalIF":2.9,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An effective operator splitting scheme for general motion by mean curvature using a modified Allen–Cahn equation","authors":"Zihan Cao,&nbsp;Zhifeng Weng,&nbsp;Shuying Zhai","doi":"10.1016/j.aml.2025.109472","DOIUrl":"10.1016/j.aml.2025.109472","url":null,"abstract":"<div><div>We present a fast and effective method for modeling general motion by mean curvature based on a modified Allen–Cahn equation. Employing the second-order operator time-splitting method, the original problem is discretized into three subproblems based on the different natures of each part of the model: the heat equation is solved by a Crank–Nicolson (CN) alternating direction implicit (ADI) finite difference scheme; the other two nonlinear equations have closed-form solutions and thus can be solved analytically. We demonstrate that the resulting scheme can preserve the maximum principle of the modified Allen–Cahn equation. Numerical experiments are presented to demonstrate the effectiveness of the proposed scheme.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109472"},"PeriodicalIF":2.9,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Novel Razumikhin-type finite-time stability criteria of fractional nonlinear systems with time-varying delay","authors":"Shuihong Xiao,&nbsp;Jianli Li","doi":"10.1016/j.aml.2025.109469","DOIUrl":"10.1016/j.aml.2025.109469","url":null,"abstract":"<div><div>This paper investigates the finite-time stability (FTS) of fractional-order nonlinear systems with time-varying delay (FONDSs). Unlike most of the existing literatures on FTS of fractional-order nonlinear delayed systems by means of establishing delayed integral inequalities, several Razumikhin-type Lyapunov conditions are presented in this paper. Using these results, we derive stability criteria for fractional-order neural networks (FONNs) and fractional-order non-autonomous systems (FONASs), respectively. Finally, two numerical examples are provided to demonstrate the applicability and effectiveness of the proposed theorems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109469"},"PeriodicalIF":2.9,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improvement of conditions for global solvability in a chemotaxis system with signal-dependent motility and generalized logistic source","authors":"Changfeng Liu ,&nbsp;Jianping Gao","doi":"10.1016/j.aml.2025.109470","DOIUrl":"10.1016/j.aml.2025.109470","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper deals with a chemotaxis system with signal-dependent motility &lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt; under homogeneous Neumann boundary conditions in a bounded domain &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. If &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; are constants, we prove that this problem possesses a global classical solution that is uniformly bounded under the conditions that &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mo&gt;min&lt;/mo&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; This result partially improved the work of Lv and Wang (Proc Roy Soc Edinburgh Sect A. 2021, 151 (2): 821-841), in which, the global boundedness of solution is established for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mf","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109470"},"PeriodicalIF":2.9,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dispersive shock waves in the fifth-order modified KdV equation","authors":"Dong-Rao Jing,&nbsp;Hai-Qiang Zhang,&nbsp;Nan-Nan Wei","doi":"10.1016/j.aml.2025.109468","DOIUrl":"10.1016/j.aml.2025.109468","url":null,"abstract":"<div><div>This study focuses on the Whitham modulation theory of the fifth-order modified KdV equation (5mKdV), successfully deriving the solutions for modulated periodic waves and establishing corresponding Whitham equations. Through the detailed analysis of the initial step solution, the rarefaction waves and two types of dispersive shock wave structures are revealed. Our results not only enrich the theoretical system of the 5mKdV equation but also provide valuable theoretical support for the analysis and control of wave phenomena.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109468"},"PeriodicalIF":2.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Localized Hermite method of approximate particular solutions for solving the Poisson equation","authors":"Kwesi Acheampong,&nbsp;Huiqing Zhu","doi":"10.1016/j.aml.2025.109471","DOIUrl":"10.1016/j.aml.2025.109471","url":null,"abstract":"<div><div>In this paper, we propose a localized Hermite method of approximate particular solutions (LHMAPS) for solving the Poisson equation. Unlike the localized method of approximate particular solutions (LMAPS) that approximates only function values of the solution in different local neighborhoods of collocation nodes by using particular solutions of radial basis functions, the proposed method employs mixed basis functions, combining radial basis functions and their particular solutions for the Laplace operator within local stencils to simultaneously approximate both the solution and its Laplacian. Numerical experiments show that significantly improves the accuracy of LMAPS.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109471"},"PeriodicalIF":2.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A class of higher-order time-splitting Monte Carlo method for fractional Allen–Cahn equation","authors":"Huifang Yuan ,&nbsp;Zhiyuan Hui","doi":"10.1016/j.aml.2025.109467","DOIUrl":"10.1016/j.aml.2025.109467","url":null,"abstract":"<div><div>In this paper, we introduce a novel class of higher-order time-splitting Monte Carlo method tailored for both fractional and classical Allen–Cahn equations. The proposed method integrates the spectral Monte Carlo method (SMC) with a time-splitting scheme, alternating between efficiently computing the linear propagator via the spectral Monte Carlo method and explicitly evaluating the nonlinear propagator. Numerical results for various <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></mrow></math></span> demonstrate the method’s ability to achieve first-, second-, and fourth-order convergence rates, thereby confirming its effectiveness and accuracy.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109467"},"PeriodicalIF":2.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the oscillation of second-order functional differential equations with a delayed damping term","authors":"Osama Moaaz ,&nbsp;Higinio Ramos","doi":"10.1016/j.aml.2025.109464","DOIUrl":"10.1016/j.aml.2025.109464","url":null,"abstract":"<div><div>In this work, we derive some criteria for studying the asymptotic and oscillatory behavior of solutions of functional differential equations with a delayed damping term. Our results extend and improve upon the limited prior research on this type of equations. The primary goal is to derive criteria applicable to both ordinary and non-damped cases, while accounting for the effects of delay functions. Additionally, unlike previous studies, we provide criteria that ensure the oscillation of all solutions. The significance of these results is illustrated through remarks and examples.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109464"},"PeriodicalIF":2.9,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Leighton–Wintner-type oscillation theorem for the discrete p(k)-Laplacian","authors":"Kōdai Fujimoto ,&nbsp;Kazuki Ishibashi ,&nbsp;Masakazu Onitsuka","doi":"10.1016/j.aml.2025.109465","DOIUrl":"10.1016/j.aml.2025.109465","url":null,"abstract":"<div><div>This paper addresses oscillation problems for difference equations with a discrete <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>-Laplacian. In general, applying the Riccati technique to discrete oscillations is difficult. However, this study established a Leighton–Wintner-type oscillation theorem using the Riccati technique. Three examples are provided to illustrate the results. In particular, we examined the oscillatory problem for a certain nonlinear difference equation, including the Harper model, and demonstrated that the solutions are oscillatory even when <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> diverges to infinity.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109465"},"PeriodicalIF":2.9,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}